An autonomously moving on-panel cleaning robot and a cleaning method. The method is applied to an on-panel cleaning robot. The method comprises: a controller controlling a cleaning machine to move along a first side edge of a panel to be cleaned, and stop moving when a first angular position of the first side edge is sensed (S1); the controller controlling the cleaning machine to rotate so as to face away from the first side edge, and start cleaning operation (S2); the controller controlling the cleaning machine to move forward along a side edge on one side of the cleaning machine, and when an angular position in the forward direction is sensed, stop moving and turn around to approach another side edge parallel to the side edge, and move forward; when the controller senses that the cleaning machine reaches a second angular position of the first side edge, the controller controlling the cleaning machine to rotate toward the first angular position (S3). The method controls the cleaning machine to perform mobile cleaning along the edges of the panel to be cleaned by means of the sensing of the controller on the relative position of the side edge and angular positions of the panel to be cleaned and the cleaning machine, so that the cleaning process of the panel to be cleaned can be realized.